Communications in Mathematical Sciences

Vanishing viscosity and the accumulation of vorticity on the boundary

J. P. Kelliher

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Abstract

We say that the vanishing viscosity limit holds in the classical sense if the velocity for a solution to the Navier-Stokes equations converges in the energy norm uniformly in time to the velocity for a solution to the Euler equations. We prove, for a bounded domain in dimension 2 or higher, that the vanishing viscosity limit holds in the classical sense if and only if a vortex sheet forms on the boundary.

Article information

Source
Commun. Math. Sci., Volume 6, Number 4 (2008), 869-880.

Dates
First available in Project Euclid: 18 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.cms/1229619674

Mathematical Reviews number (MathSciNet)
MR2511697

Zentralblatt MATH identifier
1161.76012

Subjects
Primary: 76D05: Navier-Stokes equations [See also 35Q30] 76B99: None of the above, but in this section 76D99: None of the above, but in this section

Keywords
Vanishing viscosity incompressible fluid mechanics

Citation

Kelliher, J. P. Vanishing viscosity and the accumulation of vorticity on the boundary. Commun. Math. Sci. 6 (2008), no. 4, 869--880. https://projecteuclid.org/euclid.cms/1229619674


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